A note on the off-diagonal Muckenhoupt-Wheeden conjecture
We obtain the off-diagonal Muckenhoupt-Wheeden conjec-ture for Calder´on-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal functionsatisfies the following two weight inequalities: M : Lp(v) → Lq(u) and M : Lq´(u1−q´) → Lp´(v1−p´), the...
| Autores: | , , , , |
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| Tipo de recurso: | capítulo de libro |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/64538 |
| Acceso en línea: | http://hdl.handle.net/11441/64538 https://doi.org/10.1142/9789814699693_0006 |
| Access Level: | acceso abierto |
| Palabra clave: | Haar shift operators Calderón-Zygmund operators Two-weight inequalities Testing conditions |
| Sumario: | We obtain the off-diagonal Muckenhoupt-Wheeden conjec-ture for Calder´on-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal functionsatisfies the following two weight inequalities: M : Lp(v) → Lq(u) and M : Lq´(u1−q´) → Lp´(v1−p´), then any Calderón-Zygmund operator Tand its associated truncatedmaximal operator T⋆ are bounded from Lp(v) to Lq(u). Additionally, as-suming only the second estimate for Mthen Tand T* map continuouslyLp(v) into Lq,∞(u). We also consider the case of generalized Haar shiftoperators and show that their off-diagonal two weight estimates are gov-erned by the corresponding estimates for the dyadic Hardy-Littlewoodmaximal function. |
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